Approaches to robust H ∞ static output feedback control of discrete-time piecewise-affine systems with norm-bounded uncertainties

International Journal of Robust and Nonlinear Control

Volumn 21, Issue 7, 2011, Pages 790-814

  Qiu, Jianbin ^a,b   Feng, Gang ^b   Gao, Huijun ^a  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b CITY UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

output feedback; piecewise affine systems; robust control; time varying uncertainty

Indexed keywords

CONTROLLER GAIN; DISCRETE-TIME; DISTURBANCE ATTENUATION LEVELS; MATRIX INEQUALITY; NORM-BOUNDED UNCERTAINTY; OUTPUT FEEDBACK; PARAMETERIZED; PIECEWISE LYAPUNOV FUNCTIONS; PIECEWISE-AFFINE SYSTEMS; PIECEWISE-LINEAR; ROBUST H; S-PROCEDURES; SIMULATION EXAMPLE; STATIC OUTPUT FEEDBACK; STATIC OUTPUT FEEDBACK CONTROL; TIME-VARYING PARAMETRIC UNCERTAINTIES; TIME-VARYING UNCERTAINTY;

ASYMPTOTIC STABILITY; CONTROLLERS; FEEDBACK CONTROL; LINEAR MATRIX INEQUALITIES; LYAPUNOV FUNCTIONS; NONLINEAR CONTROL SYSTEMS; PIECEWISE LINEAR TECHNIQUES; ROBUST CONTROL; TIME VARYING CONTROL SYSTEMS; UNCERTAIN SYSTEMS;

DISCRETE TIME CONTROL SYSTEMS;

EID: 79952821190     PISSN: 10498923     EISSN: 10991239     Source Type: Journal    
DOI: 10.1002/rnc.1627     Document Type: Article

References (49)

1. Chua L, Ying R,. Canonical piecewise-linear analysis. IEEE Transactions on Circuits and Systems 1983; CAS-30 (3): 125-140.
2. Chua L, Deng A,. Canonical piecewise-linear modeling. IEEE Transactions on Circuits and Systems 1986; CAS-33 (5): 511-525.
3. Saito T, Mitsubori K,. Control of chaos from a piecewise-linear hysteresis circuit. IEEE Transactions on Circuits and SystemsâI: Fundamental Theory and Applications 1995; 41 (3): 168-172.
4. Tsubone T, Saito T,. Stabilizing and destabilizing control for a piecewise-linear circuit. IEEE Transactions on Circuits and SystemsâI: Fundamental Theory and Applications 1998; 45 (2): 172-177. (Pubitemid 128745069)
5. Heemels WPMH, Camlibel MK, Schumacher JM,. On the dynamic analysis of piecewise-linear networks. IEEE Transactions on Circuits and SystemsâI: Fundamental Theory and Applications 2002; 49 (3): 315-327. (Pubitemid 34466600)
6. Imura J-I, van der Schaft A,. Characterization of well-posedness of piecewise-linear systems. IEEE Transactions on Automatic Control 2000; 45 (8): 1600-1619. (Pubitemid 32067057)
7. Imura J-I,. Classification and stabilizability analysis of bimodal piecewise affine systems. International Journal of Robust and Nonlinear Control 2002; 12 (10): 897-926. (Pubitemid 34916999)
8. Bemporad A, Ferrari-Trecate G, Morari M,. Observability controllability of piecewise affine hybrid systems. IEEE Transactions on Automatic Control 2000; 45 (10): 1864-1876. (Pubitemid 32067071)
9. Storace M, De Feo O,. Piecewise-linear approximation of nonlinear dynamical systems. IEEE Transactions on Circuits SystemsâI: Regular Papers 2004; 51 (4): 830-842.
10. Johansson M, Rantzer A,. Computation of piecewise Lyapunov quadratic functions for hybrid systems. IEEE Transactions on Automatic Control 1998; 43 (4): 555-559. (Pubitemid 128737378)
11. Rantzer A, Johansson M,. Piecewise linear quadratic optimal control. IEEE Transactions on Automatic Control 2000; 45 (4): 629-637.
12. Hassibi A, Boyd S,. Quadratic stabilization and control of piecewise-linear systems. Proceedings of the 1998 American Control Conference, Philadelphia, PA, June 1998; 3659-3664.
13. Juloski AL, Heemels MPMH, Weiland S,. Observer design for a class of piecewise linear systems. International Journal of Robust and Nonlinear Control 2007; 17 (15): 1387-1404. (Pubitemid 47509834)
14. Rodrigues L, How JP,. Observer-based control of piecewise-affine systems. International Journal of Control 2003; 76 (5): 459-477.
15. Rodrigues L, Boyd S,. Piecewise-affine state feedback for piecewise-affine slab systems using convex optimization. Systems and Control Letters 2005; 54 (9): 835-853. (Pubitemid 40915148)
16. â controller synthesis with applications to inventory control of switched production systems. Automatica 2006; 42 (8): 1245-1254. (Pubitemid 43983032)
17. Rodrigues L,. Stability of sampled-data piecewise-affine systems under state feedback. Automatica 2007; 43 (7): 1249-1256. (Pubitemid 46802433)
18. â controller synthesis for uncertain PWA slab systems: LMI approach. International Journal of Control 2009; 82 (3): 482-492.
19. Zhang J, Tang W,. Output feedback optimal guaranteed cost control of uncertain piecewise linear systems. International Journal of Robust and Nonlinear Control 2009; 19 (5): 569-590.
20. Pettersson S, Lennartson B,. Hybrid system stability and robustness verification using linear matrix inequalities. International Journal of Control 2002; 75 (16/17): 1335-1355.
21. Lin H, Antsaklis PJ,. Switching stabilizability for continuous-time uncertain switched linear systems. IEEE Transactions on Automatic Control 2007; 52 (4): 633-646. (Pubitemid 46621588)
22. Sontag ED,. Nonlinear regulation: the piecewise linear approach. IEEE Transactions on Automatic Control 1981; 26 (2): 346-357.
23. G. Ferrari-Trecate, Cuzzola FA, Mignone D, Morari M,. Analysis of discrete-time piecewise affine and hybrid systems. Automatica 2002; 38 (12): 2139-2146. (Pubitemid 35276215)
24. â analysis and control of discrete-time piecewise affine systems. International Journal of Control 2002; 75 (16-17): 1293-1301.
25. Feng G,. Stability analysis of piecewise discrete-time linear systems. IEEE Transactions on Automatic Control 2002; 47 (7): 1108-1112. (Pubitemid 34835333)
26. Feng G,. Observer based output feedback controller design of piecewise-discrete time linear systems. IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 2003; 50 (3): 448-451.
27. Xu J, Xie L, Feng G,. Feedback control design for discrete-time piecewise affine systems. Proceedings of the 2005 International Conference on Control and Automation, Budapest, Hungary, June 2005; 425-430.
28. 2 performance for discrete-time switched linear systems. International Journal of Control 2008; 81 (7): 1114-1124.
29. Feng G,. Robust filtering design of piecewise discrete time linear systems. IEEE Transactions on Signal Processing 2005; 53 (2): 599-605. (Pubitemid 40181754)
30. Feng G,. Non-synchronized state estimation of discrete time piecewise linear systems. IEEE Transactions on Signal Processing 2006; 54 (1): 295-303. (Pubitemid 43065801)
31. Zhang B, Xu S,. Robust filtering for uncertain discrete-time piecewise time-delay systems. International Journal of Control 2007; 80 (4): 636-645. (Pubitemid 46361497)
32. â filtering design for discrete-time piecewise linear delay systems. International Journal of Control 2009; 82 (1): 183-194.
33. Feng G, Zhang T,. Output regulation of discrete-time piecewise-linear systems with application to controlling chaos. IEEE Transactions on Circuits and SystemsâII: Express Briefs 2006; 54 (4): 249-253. (Pubitemid 46511164)
34. Zhang T, Feng G,. Output tracking of piecewise-linear systems via error feedback regulator with application to synchronization of nonlinear Chua's circuit. IEEE Transactions on Circuits and SystemsâI: Regular Papers 2007; 54 (8): 1852-1863. (Pubitemid 47272705)
35. Syrmos VL, Abdallah CT, Dorato P, Grigoriadis K,. Static output feedbackâa survey. Automatica 1997; 33 (2): 125-137.
36. Dong J, Yang G-H,. Static output feedback control synthesis for linear systems with time-invariant parametric uncertainties. IEEE Transactions on Automatic Control 2007; 52 (10): 1930-1936. (Pubitemid 350130535)
37. Daafouz J, Riedinger P, Iung C,. Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach. IEEE Transactions on Automatic Control 2002; 47 (11): 1883-1887. (Pubitemid 35422587)
38. â output feedback stabilization of linear discrete-time systems. IEEE Transactions on Automatic Control 2006; 51 (4): 675-680.
39. Dong J, Yang G-H,. Robust static output feedback control for linear discrete-time systems with time-varying uncertainties. Systems and Control Letters 2008; 57 (2): 123-131. (Pubitemid 350251625)
40. Ding D-W, Yang G-H,. Static output feedback control for discrete-time piecewise linear systems: an LMI approach. Acta Automatica Sinica 2009; 35 (4): 337-344.
41. â performance for linear discrete-time systems. IEEE Transactions on Automatic Control 2005; 50 (2): 250-254. (Pubitemid 40319358)
42. Bara GI, Boutayeb M,. Switched output feedback stabilization of discrete-time switched systems. Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, CA, U.S.A., December 2006; 2667-2672. (Pubitemid 351283547)
43. Bara GI,. Robust switched static output feedback control for discrete-time switched linear systems. Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, U.S.A., December 2007; 4986-4992. (Pubitemid 351283290)
44. â output-feedback of discrete-time LTI systems with state multiplicative noise. Systems and Control Letters 2006; 55 (3): 232-239. (Pubitemid 43107558)
45. Boyd S, El Ghaoui L, Feron E, Balakrishnan V,. Linear Matrix Inequality in Systems and Control Theory. SIAM: Philadelphia, PA, 1994.
46. Gahinet P, Nemirovski A, Laud A, Chilali M,. LMI Control Toolbox User's Guide. Mathworks: Natick, MA, 1995.
47. â filtering for uncertain discrete-time systems. Automatica 2004; 40 (5): 873-880.
48. â filtering for uncertain linear systems. Automatica 2006; 42 (11): 1919-1926. (Pubitemid 44436051)
49. â control of systems with parameter uncertainty. International Journal of Control 1996; 63 (4): 741-750. (Pubitemid 126519393)